Effective modelling of polar array
If you run this baby script:

import bpy

idx = 1
vtx = 6
rad = 0.25
inc = 0.25

while (idx &lt; 14):
    bpy.ops.mesh.primitive_circle_add(vertices=vtx, radius=rad)
    rad += inc
    vtx += 6
    idx += 1 


It will create a series of concentric circles with the right number of vertices. (I'm sure a proper Pythonista could do it in one line, and automate some of the steps which follow...)


CtrlJ Join the circles into one object
CtrlE > Bridge Edge Loops each pair of loops in turn, and F..AltP, fan-fill the center.
You wind up with a mesh with one or two diagonals out of place. I'm not sure it would matter, but I cut 1/6 out as shown, corrected the edges, and arrayed it back to a full circle)
Select all vertices except those on the perimeter, and CtrlShiftB bevel them, and switch to Face mode. The future holes should be selected.
Loop-Tools or Space-Bar > 'Circle' with a radius setting, on the selected hole-faces.
Delete the faces
Extrude or add a Solidify modifier, and throw on a Subdivision modifier. 




The holes aren't perfectly circular but maybe good enough?